Question

If f(x) = 2x + 1 and g(x) = x² + 2x + 1, find g(f(x)).

Answer 1

g(f(x)) = 4x^2 + 8x + 4

Explanation:

If f(x) = 2x + 1 and g(x) = x² + 2x + 1, find g(f(x)).

You are asked to find g of f of x.

This means your x value for the equation g(x) is f(x), hence g(f(x)).

g(2x+1)=(2x+1)^2 + 2(2x+1) +1

g(2x+1) = 4x^2 + 4x + 1 +4x + 2 + 1

Combine like terms.

g(2x+1) = 4x^2 + 8x + 4

g(f(x)) = 4x^2 + 8x + 4